Nonperturbative Effects in Superstring Theory

我们研究的主要问题是非对易场论与无穷多D-膜的构形性质之间的关系。D-膜是弦理论中的孤子解。在某些维度上的D-膜可以描述为无限多个低维D-膜的配置。我们已经用微扰弦理论证明了这一事实。我们还讨论了D-膜的几何性质如重参数化不变性是如何在低维膜的描述中实现的，D-膜的涨落通常用Yang-Mills理论来描述。然而，在NS阶反对称张量场为常数的背景下，我们应该使用所谓的非对易Yang-Mills理论，它是Yang-Mills理论在非对易坐标空间上的推广。我们证明了，如果把D-膜看作是无限多个低维膜的构形，或者使用矩阵模型，这个事实就可以很自然地理解。我们还表明，这样的描述是有用的，在构建规范不变的观测量的理论，或理解微扰方面的理论。此外，在矩阵模型中，四维非对易杨-米尔斯理论可以被认为是矩阵模型在四维时空中的实现。我们讨论了引力相互作用是如何在这样的理论中实现的，我们还研究了非紧曲流形上的弦理论。

The main topic, we have studied is the relation between the noncommutative field theory and the nature of the configurations of infinitely many D-branes. D-branes are soliton solutions in string theory. A D-brane in certain dimensions can be described as a configuration of infinitely many lower dimensional D-branes. we have shown this fact using perturbative string theory. We also discussed how the geometrical aspects of a D-brane such as reparametrization invariance are realized in the description using lower dimensional branes.Usually the fluctuations of D-branes are described by using Yang-Mills theory. However, in a background of constant NS antisymmetric tensor field, we should use so-called noncommutative Yang-Mills theory, which is a generalization of Yang-Mills theory on a space with noncommutative coordinates. We showed that this fact can be understood naturally if one consider the D-brane as a configuration of infinitely many lower dimensional branes or by using matrix models. We also showed that such descriptions are useful in constructing the gauge invariant observables of the theory, or understanding the perturbative aspects of the theory. Moreover, in the matrix model context, 4 dimensional noncommutative Yang-Mills theory can be considered as a realization of the matrix model in 4 spacetime dimensions. We have discussed how gravitational interactions are realized in such a theory.We also studied string theory on a noncompact curved manifold.